GCF of 35 and 42
GCF of 35 and 42 is the largest possible number that divides 35 and 42 exactly without any remainder. The factors of 35 and 42 are 1, 5, 7, 35 and 1, 2, 3, 6, 7, 14, 21, 42 respectively. There are 3 commonly used methods to find the GCF of 35 and 42 - Euclidean algorithm, prime factorization, and long division.
| 1. | GCF of 35 and 42 |
| 2. | List of Methods |
| 3. | Solved Examples |
| 4. | FAQs |
What is GCF of 35 and 42?
Answer: GCF of 35 and 42 is 7.
Explanation:
The GCF of two non-zero integers, x(35) and y(42), is the greatest positive integer m(7) that divides both x(35) and y(42) without any remainder.
Methods to Find GCF of 35 and 42
Let's look at the different methods for finding the GCF of 35 and 42.
- Using Euclid's Algorithm
- Prime Factorization Method
- Long Division Method
GCF of 35 and 42 by Euclidean Algorithm
As per the Euclidean Algorithm, GCF(X, Y) = GCF(Y, X mod Y)
where X > Y and mod is the modulo operator.
Here X = 42 and Y = 35
- GCF(42, 35) = GCF(35, 42 mod 35) = GCF(35, 7)
- GCF(35, 7) = GCF(7, 35 mod 7) = GCF(7, 0)
- GCF(7, 0) = 7 (∵ GCF(X, 0) = |X|, where X ≠ 0)
Therefore, the value of GCF of 35 and 42 is 7.
GCF of 35 and 42 by Prime Factorization
Prime factorization of 35 and 42 is (5 × 7) and (2 × 3 × 7) respectively. As visible, 35 and 42 have only one common prime factor i.e. 7. Hence, the GCF of 35 and 42 is 7.
GCF of 35 and 42 by Long Division
GCF of 35 and 42 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.
- Step 1: Divide 42 (larger number) by 35 (smaller number).
- Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (35) by the remainder (7).
- Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (7) is the GCF of 35 and 42.
☛ Also Check:
- GCF of 54 and 90 = 18
- GCF of 8 and 14 = 2
- GCF of 24 and 42 = 6
- GCF of 28 and 48 = 4
- GCF of 63 and 54 = 9
- GCF of 39 and 6 = 3
- GCF of 15 and 27 = 3
FAQs on GCF of 35 and 42
What is the GCF of 35 and 42?
The GCF of 35 and 42 is 7. To calculate the greatest common factor (GCF) of 35 and 42, we need to factor each number (factors of 35 = 1, 5, 7, 35; factors of 42 = 1, 2, 3, 6, 7, 14, 21, 42) and choose the greatest factor that exactly divides both 35 and 42, i.e., 7.
How to Find the GCF of 35 and 42 by Prime Factorization?
To find the GCF of 35 and 42, we will find the prime factorization of the given numbers, i.e. 35 = 5 × 7; 42 = 2 × 3 × 7.
⇒ Since 7 is the only common prime factor of 35 and 42. Hence, GCF (35, 42) = 7.
☛ What are Prime Numbers?
How to Find the GCF of 35 and 42 by Long Division Method?
To find the GCF of 35, 42 using long division method, 42 is divided by 35. The corresponding divisor (7) when remainder equals 0 is taken as GCF.
What are the Methods to Find GCF of 35 and 42?
There are three commonly used methods to find the GCF of 35 and 42.
- By Listing Common Factors
- By Prime Factorization
- By Long Division
What is the Relation Between LCM and GCF of 35, 42?
The following equation can be used to express the relation between LCM and GCF of 35 and 42, i.e. GCF × LCM = 35 × 42.
If the GCF of 42 and 35 is 7, Find its LCM.
GCF(42, 35) × LCM(42, 35) = 42 × 35
Since the GCF of 42 and 35 = 7
⇒ 7 × LCM(42, 35) = 1470
Therefore, LCM = 210
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